A Curved Brunn Minkowski Inequality for the Symmetric Group

The Brunn-Minkowski-Type Inequality

The Infinitesimal Form of Brunn-minkowski Type Inequalities

Log-Brunn-Minkowski inequality was conjectured by Boröczky, Lutwak, Yang and Zhang [7], and it states that a certain strengthening of the classical Brunn-Minkowski inequality is admissible in the case of symmetric convex sets. It was recently shown by Nayar, Zvavitch, the second and the third authors [27], that Log-Brunn-Minkowski inequality implies a certain dimensional Brunn-Minkowski inequal...

Volume difference inequalities for the projection and intersection bodies

In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.

A Curved Brunn-Minkowski Inequality on the Discrete Hypercube, Or: What Is the Ricci Curvature of the Discrete Hypercube?

We compare two approaches to Ricci curvature on nonsmooth spaces in the case of the discrete hypercube {0, 1}N . While the coarse Ricci curvature of the first author readily yields a positive value for curvature, the displacement convexity property of Lott, Sturm, and Villani could not be fully implemented. Yet along the way we get new results of a combinatorial and probabilistic nature, includ...

A Curved Brunn–minkowski Inequality on the Discrete Hypercube Or: What Is the Ricci Curvature of the Discrete Hypercube? Y. Ollivier and C. Villani

We compare two approaches to Ricci curvature on non-smooth spaces, in the case of the discrete hypercube {0, 1} . While the coarse Ricci curvature of the first author readily yields a positive value for curvature, the displacement convexity property of Lott, Sturm and the second author could not be fully implemented. Yet along the way we get new results of a combinatorial and probabilistic natu...